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Dynamic Modelling

The static models to determine critical loads consider only the stead-state condition, in which the chemical and biological response to a change in deposition is complete. Dynamic models on the other hand, attempt to estimate the time required for a new (steady) state to be achieved

With critical loads, i.e. in the steady-state situation, only two cases can be distinguished when comparing them to deposition: (1) the deposition is below critical load(s), i.e. does not exceed critical loads, and (2) the deposition is greater than critical load(s), i.e. there is critical load exceedance. In the first case there is no (apparent) problem, i.e. no reduction in deposition is deemed necessary. In the second case there is, by definition, an increased risk of damage to the ecosystem, and therefore the deposition should be reduced. A critical load serves as a warning as long as there is exceedance, since it tells that deposition should be reduced. However, it is often assumed that reducing deposition to (or below) critical loads immediately removes the risk of 'harmful effects', i.e. the chemical parameter (e.g. the Al:Bc ratio), which links the critical load to the effect(s), immediately attains a non-critical ('safe') value and that there is immediate biological recovery as well. But the reaction of soils, especially their solid phase, to changes in deposition is delayed by (finite) buffers, the most important being the cation exchange capacity (CEC). The buffer mechanisms can delay the attainment of a critical chemical parameter, and it might take decades or even centuries, before an equilibrium (steady state) is reached. These finite buffers are not included in the critical load formulation, since they do not influence the steady state, but only the time to reach it. Therefore, dynamic models are needed to estimate the times involved in attaining a certain soil chemical state in response to deposition scenarios, e.g., the consequences of 'gap closures' in emission reduction negotiations. In addition to the delay in chemical recovery, there is likely to be a further delay before the 'original' biological state is reached, i.e. even if the chemical criterion is met (e.g. Al:Bc<1), it will take time before full biological recovery is achieved.

fig 4 dyn mod

Figure 4 summarises the possible development of a (soil) chemical and biological variable in response to a 'typical' temporal deposition pattern. Five stages can be distinguished:

Stage 1
Deposition was and is below the critical load (CL) and the chemical and biological variables do not violate their respective criteria. As long as deposition stays below the CL, this is the 'ideal' situation.

Stage 2
Deposition is above the CL, but the chemical and biological variables are still below the critical value. There is no risk for 'harmful effects' yet; there is a delay before the criteria are violated. Therefore, damage is not visible in this stage, despite the exceedance of the CL. We call the time between the first exceedance of the CL and first violation of the biological criterion (the first occurrence of actual damage) the Damage Delay Time (DDT=t3-t1).

Stage 3
The deposition is above CL and both the chemical and biological criteria are violated. Measures have to be taken to avoid a (further) deterioration of the ecosystem.

Stage 4
Deposition is below the CL, but the chemical and biological criteria are still violated, and thus recovery has not yet occurred. We call the time between the first non-exceedance of the CL and the subsequent non-violation of both criteria the Recovery Delay Time (RDT=t6-t4).

Stage 5
This stage is similar to Stage 1. Deposition is below the CL and both criteria are no longer violated. Only at this stage can one speak of full ecosystem recovery.

Stages 2 and 4 can be further subdivided into two sub-stages each: Chemical delay times (DDTc=t2-t1 and RDTc=t5-t4; dark grey in Fig.4) and (additional) biological delay times (DDTb=t3-t2 and RDTb=t6-t5; light grey). In the near future, due to the lack of operational biological response models, damage and recovery delay times will mostly refer to chemical recovery alone and they will be used as a surrogate for overall recovery.

A Dynamic Modelling Manual provides information for National Focal Centres and their collaborating institutes on the background, concepts and data requirements for dynamic modelling in support of the work under the LRTAP Convention. An updated version can also be found as Chapter 6 of the Mapping Manual.

last update 5 Jun 2013